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N is a 2-digit number. When N is divided by 2, the remainder

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by Max@Math Revolution » Mon Sep 02, 2019 11:24 pm

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[GMAT math practice question]

N is a 2-digit number. When N is divided by 2, the remainder is 1, when it is divided by 3 the remainder is 2, and when it is divided by 5 the remainder is 4. What is the sum of all possible values of N?

A. 155
B. 166
C. 177
D. 188
E. 200
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by Max@Math Revolution » Wed Sep 04, 2019 11:45 pm
=>

Using the quotient-remainder theorem, we may write n as 2a + 1, 3b + 2, and 5c + 4, where a, b and c are non-negative integers.
The possible values of 2a + 1 are 1, 3, 5, ... .
The possible values of 3b + 2 are 2, 5, 8, 11, ...
The possible values of 5c + 4 are 4, 9, 14, 19, 24, 29, ...
Since the first common value from these lists is 29 and the least common multiple of 2, 3 and 5 is 30, N is an integer of the form 30k + 29.
The possible values of N with 2 digits are 29, 59 and 89.
Thus, the sum of all possible values of N is 29 + 59 + 89 = 177.

Therefore, C is the answer.
Answer: C
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